# Ternary computer

A **ternary computer** (also called **trinary computer**) is a computer that uses ternary logic (three possible values) and trits instead of the more common binary logic (two possible values) and bits in its calculations.

## History

One early calculating machine, built by Thomas Fowler entirely from wood in 1840, operated in balanced ternary.^{[1]}^{[2]} The first modern, electronic ternary computer Setun was built in 1958 in the Soviet Union at the Moscow State University by Nikolay Brusentsov,^{[3]}^{[4]} and it had notable advantages over the binary computers which eventually replaced it, such as lower electricity consumption and lower production cost.^{[3]} In 1970 Brusentsov built an enhanced version of the computer, which he called Setun-70.^{[3]} In the USA, the ternary computing emulator Ternac working on a binary machine was developed in 1973.

The ternary computer QTC-1 was developed in Canada.^{[5]}

## Balanced ternary

Ternary computing is commonly implemented in terms of balanced ternary, which uses the three digits −1, 0, and +1. The negative value of any balanced ternary digit can be obtained by replacing every + with a − and vice versa. It is easy to subtract a number by inverting the + and − digits and then using normal addition. Balanced ternary can express negative values as easily as positive ones, without the need for a leading negative sign as with decimal numbers. These advantages make some calculations more efficient in ternary than binary. Considering that digit signs are mandatory, and nonzero digits are magnitude 1 only, notation using only zero and signs alone is more concise than when 1's are used.

I often reflect that had the Ternary instead of the denary Notation been adopted in the Infancy of Society, machines something like the present would long ere this have been common, as the transition from mental to mechanical calculation would have been so very obvious and simple.

## Potential future applications

With the advent of mass-produced binary components for computers, ternary computers have diminished in significance. However, Donald Knuth argues that they will be brought back into development in the future to take advantage of ternary logic's elegance and efficiency.^{[6]} One possible way this could happen is by combining an optical computer with the ternary logic system.^{[7]} A ternary computer using fiber optics could use dark as 0 and two orthogonal polarizations of light as 1 and −1. IBM also reports infrequently on ternary computing topics (in its papers), but it is not actively engaged in it.

The Josephson junction has been proposed as a balanced ternary memory cell, using circulating superconducting currents, either clockwise, counterclockwise, or off. "The advantages of the proposed memory circuit are capability of high speed computation, low power consumption and very simple construction with fewer elements due to the ternary operation."^{[8]}

In 2009, a quantum computer was proposed which uses a quantum ternary state, a qutrit, rather than the typical qubit. When the number of basic states of quantum element is *d*, it is called qudit.^{[9]}

## Ternary computers in popular culture

In Robert A. Heinlein's novel *Time Enough for Love*, the sapient computers of Secundus, the planet on which part of the framing story is set, including Minerva, use an unbalanced ternary system. Minerva, in reporting a calculation result, says "three hundred forty one thousand six hundred forty... the original ternary readout is unit pair pair comma unit nil nil comma unit pair pair comma unit nil nil point nil".^{[10]}

Virtual Adepts in the roleplaying game *Mage: The Ascension* use ternary computers.

In Howard Tayler's webcomic *Schlock Mercenary*, every modern computer is a ternary computer. AIs use the extra digit as "maybe" in boolean (true/false) operations, thus having a much more intimate understanding of fuzzy logic than is possible with binary computers.

The Conjoiners, in Alastair Reynolds' *Revelation Space* series, use ternary logic to program their computers and nanotechnology devices.

## Further reading

- Hunger, Francis (2007).
*Eine Recherche über den sowjetischen Ternarcomputer*[*SETUN. An Inquiry into the Soviet Ternary Computer*]. Institut für Buchkunst Leipzig. ISBN 3-932865-48-0. Also (in German)

## See also

## References

- ↑ "Thomas Fowler biography". Archived from the original on 31 May 2007.
- 1 2 Glusker, Mark; Hogan, David M.; Vass, Pamela (July–September 2005). "The Ternary Calculating Machine of Thomas Fowler".
*IEEE Annals of the History of Computing*.**27**(3): 4–22. doi:10.1109/mahc.2005.49. - 1 2 3 Russian Virtual Computer Museum – Hall of Fame – Nikolay Petrovich Brusentsov, retrieved 2010-01-25.
- ↑ Trogemann, Georg; Nitussov, Alexander Y.; Ernst, Wolfgang (2001),
*Computing in Russia: the history of computer devices and information technology revealed*, Vieweg+Teubner Verlag, pp. 19, 55, 57, 91, 104–107, ISBN 978-3-528-05757-2. - ↑ Y. H. Cho; and H. T. Mouftah. "A CMOS ternary chip".
- ↑ Knuth, D.E.
*The Art of Computer Programming – Volume 2*: Seminumerical Algorithms, pp. 190–192. Addison-Wesley, 2nd ed., 1980. ISBN 0-201-03822-6. - ↑ Jin Yi; He Huacan; Lü Yangtian (2005). "Ternary Optical Computer Architecture".
*Phys. Scripta*.**2005**(98). doi:10.1238/Physica.Topical.118a00098. - ↑ "A Josephson ternary memory circuit".
*Proceedings. 1998 28th IEEE International Symposium on Multiple- Valued Logic (Cat. No.98CB36138)*. doi:10.1109/ISMVL.1998.679270. - ↑ Qudits at NextBigFuture.com
- ↑ Heinlein, Robert A. (1982). "Variations on a Theme III: Domestic Problems".
*Time Enough for Love*. Berkley Books. p. 99. ISBN 0-399-11151-4. - ↑ Ternary "flip-flap-flop"

## External links

- ROLUAN - Ternary ecosystem startup. Ternary software and hardware
- Tunguska - Ternary Operating System emulator
- 3niti - Collaboration for Open Ternary Computer Development
- Development of ternary computers at Moscow State University
- The ternary calculating machine of Thomas Fowler
- Ternary Optical computer
- Jeff Connelly (2008). "Ternary Computing Testbed 3-Trit Computer Architecture" (PDF). (6.6 MB)